Writing and Solving Math Problems

Let $J$ problems/hour be the speed at which John writes math problems. Then $\frac{J}{2}$ problems/hour is the speed at which he solves them. Let $L$ problems/hour be the speed at which Jill writes math problems. Then $2L$ is the rate at which she solves math problems.

We're given that, in one hour, they write 100 math problems altogether: $J + L = 100.$ Similarly, the combined number of problems that they'll solve in one hour is $\frac{J}{2} + 2L = 100.$

Solving these simultaneous equations:
$\frac{J}{2} + 2L = 100$
$\frac{J}{2} + 2(100-J) = 100$
$\frac{J}{2} + 200 - 2J = 100$
$\frac{J}{2} + 200 - \frac{4J}{2} = 100$
$100 = \frac{3J}{2}$ $66.6 = J, 33.3 = L$

Therefore, Jack writes problems twice as quickly as Jill.